On the Tractability of the Measure Associated to the Phase-Type Planar Point Process

Abstract

One primary purpose of introducing the phase-type planar point process was to offer an algorithmically tractable point process on the plane. In an attempt to achieve this objective, we describe here a powerful technique to obtain the distribution and the moments of the number of points generated by the process and located in a particular convex bounded Borel set of the plane. Applied to the case of the circle, this technique has enabled us to estimate the outage probability in a CDMA based wireless system. Furthermore, a numerical analysis of the second moment of the number of points in a circle is discussed. This analysis highlights among others some relevant asymptotic results and therefore ways to distinguish between the processes. The technique we derive here can be exploited in many different problems as illustrated in our conclusion.